Theme Essential Question: How do we use a system of equations to model real world situations that have multi-constraints to simulate relationships?
Essential Questions: How systems of equations are represented and interpreted using technology?
Standards Analyze and solve pairs of simultaneous linear equations.
8. EE.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
8. EE.8c Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.
Objectives
The student will use technology to prepare a graphical representation to interpret the solution to a system of linear equations.
The students will investigate the outcome of linear equations that intersect, coincide, or are parallel.
Assessment Product http://mwstrange.com/Systems%20of%20Linear%20Equations%20Group%20Project.pdf In this project the students will be choosing between two real life situations and then using systems of linear equations to decide what to buy. Please be advised computer access will be advantageous. Week 1: Teacher introduction to the project and rubric. Week 2: Students thoroughly exploring and selecting their project. Option: Cell Phone Plans Encourage students to explore and compare other company plans and vary the options available. Option: Car Comparisons Encourage students to explore and compare other cars. Week 3: Students will conduct research and apply a graphical solution to their project (manually or using technology). Week 4: Students will support their solution by using the substitution method and/or the elimination method to their project. Week 5: Students will analyze their solution, complete their project, and conduct presentations.
Key Questions
Using technology, what is the process to represent and interpret a solution to a system of linear equations?
What conclusions can be made when the system of linear equations intersect, coincide, or are parallel?
Observable Student Behaviors
Students can use technology to graph and interpret a solution to a system of linear equations.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Vocabulary System of equations, coordinate plane, slope, y intercept, slope-intercept form
Suggested Activities [see Legend to highlight MCO and HYS]
Houghton Mifflin OnCore Mathematics Middle School Grade 8
Unit 3.3, p. 75-78
ABC Mastering the Common Core in Mathematics 6.1- p. 76-78
Gizmo Lessons
8.EE.8a
Solving Linear Systems by Graphing
Compare a system of equations in standard form or in slope‑intercept form to its graph. Examine the graph and table of values. Determine the solutions to the system.
Special Types of Solutions to Linear Systems
Compare a system of equations in standard form to its graph. Examine the graph and table of values. Determine the solutions to the system.
Teaching the Common Core Math Standards with Hands-On Activities by Judith Muschla
Content: Solving Systems Graphically (Technology)
Dates:4/15-4/19
Theme Essential Question:
How do we use a system of equations to model real world situations that have multi-constraints to simulate relationships?
Essential Questions:
How systems of equations are represented and interpreted using technology?
Standards
Analyze and solve pairs of simultaneous linear equations.
Objectives
Assessment
Product
http://mwstrange.com/Systems%20of%20Linear%20Equations%20Group%20Project.pdf
In this project the students will be choosing between two real life situations and then using systems of linear equations to decide what to buy. Please be advised computer access will be advantageous.
Week 1: Teacher introduction to the project and rubric.
Week 2: Students thoroughly exploring and selecting their project.
Option: Cell Phone Plans
Encourage students to explore and compare other company plans and vary the options available.
Option: Car Comparisons
Encourage students to explore and compare other cars.
Week 3: Students will conduct research and apply a graphical solution to their project (manually or using technology).
Week 4: Students will support their solution by using the substitution method and/or the elimination method to their project.
Week 5: Students will analyze their solution, complete their project, and conduct presentations.
Key Questions
Observable Student Behaviors
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary
System of equations, coordinate plane, slope, y intercept, slope-intercept form
Suggested Activities [see Legend to highlight MCO and HYS]
- Houghton Mifflin OnCore Mathematics Middle School Grade 8
Unit 3.3, p. 75-78- ABC Mastering the Common Core in Mathematics 6.1- p. 76-78
Gizmo Lessons- 8.EE.8a
- Solving Linear Systems by Graphing
- Compare a system of equations in standard form or in slope‑intercept form to its graph. Examine the graph and table of values. Determine the solutions to the system.
- Special Types of Solutions to Linear Systems
- Compare a system of equations in standard form to its graph. Examine the graph and table of values. Determine the solutions to the system.
Teaching the Common Core Math Standards with Hands-On Activities by Judith Muschla- 8.EE.8 Activity 1 p. 180, Activity 2 p. 181
Glencoe Pre-Algebra – p. 414-418, p. 428Glencoe Algebra 1- p. 369-375
- Highly Recommended:
http://illustrativemathematics.org/illustrations/469 (G.8)http://illustrativemathematics.org/illustrations/472 (G.8)
http://illustrativemathematics.org/illustrations/554 (G.8)
http://illustrativemathematics.org/illustrations/73 (G.8)The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
Diverse Learners
Homework
Suggested:
Terminology for Teachers
Ethnicity/Culture | Immigration/Migration | Intercultural Competence | Socialization | Racism/Discrimination
High Yield Strategies
Similarities/Differences | Summarizing/Notetaking | Reinforcing/Recognition | Homework/Practice |
Non-Linguistic representation | Cooperative Learning | Objectives/Feedback |
Generating-Testing Hypothesis | Cues, Questions, Organizers
Resources
Professional Texts
Literary Texts
Informational Texts
- See New York Common Core Aligned Task (other resources)
http://schools.nyc.gov/Academics/CommonCoreLibrary/SeeStudentWork/default.htmArt, Music, and Media
Manipulatives
Games
Videos
SMART Board Lessons, Promethean Lessons
- Smartboard Resource Website Smartboard lesson search engine
- 8. EE.8a Solving Systems of Equations through Graphing
Solve systems of two linear equations in two variables by graphing. Interpret solutions of two linear equations.- 8. EE.8c Solving Problems Involving Algebraic Techniques (Question Set)
Solving Problems Involving Algebraic Techniques (Question set)Websites
Other Activities, etc.
Language
Arts
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Week 4
Week 5
Week 6
Matrix
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Week 4
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Week 6
Home K-2
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Home 6-8
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6